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For a symmetric matrix A, the vector vec(A) contains more information than is strictly necessary, since the matrix is completely determined by the symmetry together with the lower triangular portion, that is, the n(n + 1)/2 entries on and below the main diagonal. For such matrices, the half-vectorization is
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant. The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:
A formula editor is a computer program that is used to typeset mathematical formulas and mathematical expressions. Formula editors typically serve two purposes: They allow word processing and publication of technical content either for print publication, or to generate raster images for web pages or screen presentations.
A generalization of this theorem is the Helmholtz decomposition theorem, which states that any vector field can be decomposed as a sum of a solenoidal vector field and an irrotational vector field. By analogy with the Biot-Savart law , A ″ ( x ) {\displaystyle \mathbf {A''} (\mathbf {x} )} also qualifies as a vector potential for v ...
(The Center Square) – The Georgia Court of Appeals removed Fulton County District Attorney Fani Willis from prosecuting the election interference case against Donald J. Trump and others. The ...
Moviegoers can score free popcorn this weekend at AMC, Regal and more theaters. News. News. Associated Press. Bolivian judge orders the arrest of former President Morales in sex abuse case.
Directs a review of NAFTA and other free trade agreements. Read Order Read article ; April 29, 2017 Establishment of Office of Trade and Manufacturing Policy. Creates a trade policy office within the White House. Read Order Read article ; April 29, 2017 Implementing an America-First Offshore Energy Strategy
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